28,558 research outputs found
Cancellation of divergences in unitary gauge calculation of process via one W loop, and application
Following the thread of R. Gastmans, S. L. Wu and T. T. Wu, the calculation
in the unitary gauge for the process via one W loop is
repeated, without the specific choice of the independent integrated loop
momentum at the beginning. We start from the 'original' definition of each
Feynman diagram, and show that the 4-momentum conservation and the Ward
identity of the W-W-photon vertex can guarantee the cancellation of all terms
among the Feynman diagrams which are to be integrated to give divergences
higher than logarithmic. The remaining terms are to the most logarithmically
divergent, hence is independent from the set of integrated loop momentum. This
way of doing calculation is applied to process via one W loop
in the unitary gauge, the divergences proportional to including
quadratic ones are all cancelled, and terms proportional to are
shown to be zero. The way of dealing with the quadratic divergences
proportional to in has subtle implication on the
employment on the Feynman rules especially when those rules can lead to high
level divergences. So calculation without integration on all the
functions until have to is a more proper or maybe necessary way of the
employment of the Feynman rules.Comment: 1 figure, 34 pages (updated
Entanglement-guided architectures of machine learning by quantum tensor network
It is a fundamental, but still elusive question whether the schemes based on
quantum mechanics, in particular on quantum entanglement, can be used for
classical information processing and machine learning. Even partial answer to
this question would bring important insights to both fields of machine learning
and quantum mechanics. In this work, we implement simple numerical experiments,
related to pattern/images classification, in which we represent the classifiers
by many-qubit quantum states written in the matrix product states (MPS).
Classical machine learning algorithm is applied to these quantum states to
learn the classical data. We explicitly show how quantum entanglement (i.e.,
single-site and bipartite entanglement) can emerge in such represented images.
Entanglement characterizes here the importance of data, and such information
are practically used to guide the architecture of MPS, and improve the
efficiency. The number of needed qubits can be reduced to less than 1/10 of the
original number, which is within the access of the state-of-the-art quantum
computers. We expect such numerical experiments could open new paths in
charactering classical machine learning algorithms, and at the same time shed
lights on the generic quantum simulations/computations of machine learning
tasks.Comment: 10 pages, 5 figure
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